I think you did great to set ground rules. If he wants to live together, he needs to help with the situation, not making it worse (especially for kids). You did the right thing focusing on your daughter and not on him during his tantrum.
Not sure if it is possible, but you may want to find appropriate time when he is not angry, and tell him that this kind of behavior is unacceptable. You do not need to accuse him of anything. Just point out you agreed to keep the kids out of your conflicts and him screaming in front of the kids is unacceptable. He may scream again, do not retort, but do not back down either.
